Dynamic Analysis Of Functionally Graded Timoshenko Beam By The Finite Element Method

Functionally graded materials (FGMs) is a new kind of inhomogeneous composite materials with the continuously varying material property induced by the spatial distribution of their components. Due to their unique graded feature, FGMs beam-like structures have become attractive for potential applications as structural and functional elements in aerospace engineering, chemical engineering, civil engineering as well as many other engineering.In the thesis, the dynamic characteristics of functionally graded beam with material graduation through the thickness following a simple power law distribution are investigated. The system of equations of motion is derived by applying the Darren Bell’s principle into the principle of virtual work under the assumptions of the Timoshenko beam theory. For the functionally graded Timoshenko beam, a general finite element pattern is developed to analyze the fundamental frequencies of free vibration with different boundaries, slenderness ratios, element numbers, different material distribution, etc. The differences and contributions of the fundamental frequencies induced by those factors mentioned above are also discussed.The problem of shear locking usually caused by the high slenderness ratio of Timoshenko beam is well considered and solved by way of assumed shear strain and using high order elements. The selective interpolation function scheme, i.e., a three-node beam element with8degrees of freedom, is also tried for shear locking problem. Some numerical examples available in published literature are carried out to study the performance of the proposed method. The numerical results show that the proposed method has very good capability for dynamic analysis of thin to thick functionally graded beam.